How would you store a dictionary of 100,000 words and check if a word exists? A hash set gives lookup where is word length. Good enough?
Now try these: Find all words starting with "pre". Find all words that match "c_t" (any letter in the middle). Count words with a given prefix.
Hash sets struggle with prefix queries. Tries solve these problems. Each node represents a character, and paths from root to nodes spell out prefixes.
All words with prefix "pre" live in the subtree under p→r→e. Operations on tries take time. Independent of dictionary size. This makes tries needed for:
- Autocomplete systems
- Spell checkers
- IP routing tables
- Word games (Boggle, Scrabble)